Instead of dynamic programming (which would be challenging in this
infinite memory setting), our methodology is based on duality. For the
case of exponential utility and quadratic transaction costs, this
theory is developed with flexible information flow in great generality
in an essentially self-contained appendix. It shows that the primal
optimal control is determined by the conditional expectation of the
terminal stock price under the dual optimal probability measure. For
the Brownian framework that we focus on in the main body of the paper,
we derive a particularly convenient representation of the dual target
functional which leads to deterministic variational
problems. These problems can be solved explicitly, and results from the
theory of Gaussian Volterra integral equations ([1]}, [2]})
allow us both to construct the solution to the dual problem and to
compute the primal optimal strategy.
